The movable element of a solenoid valve is displaced by means of application to the solenoid of alternating phases at constant voltage and at zero voltage, so as to give rise to an alternation of phases of charging and discharging of the solenoid (switching), corresponding to increases and decreases of current around a substantially constant current value. The alternating phases at constant voltage and at zero voltage are controlled so that the phase at constant voltage is maintained for a pre-set time and the phase at zero voltage is terminated when the decreasing current reaches a pre-set value. Alternatively, it is possible to envisage that the phase at constant voltage will be terminated when the increasing current reaches a pre-set value and the phase at zero voltage is maintained for a pre-set time, or else again that both the phase at constant voltage and the phase at zero voltage will be terminated when the increasing current or decreasing current reaches a pre-set value. In any case, the duration of each cycle of charging and discharging of the solenoid is constantly monitored. It is thus possible to identify the instant at which the movable element of the solenoid valve reaches its end-of-travel position as the instant that separates two successive cycles of charging and discharging of the solenoid having durations that differ from one another by a value higher than a pre-set threshold value.